Saturday, 30 June 2012

The 182nd day of the year; there are 182 connected bipartite graphs with 8 vertices. *What's So Special About This Number

EVENTS

1737 John Harrison, after positive results on the test of his first sea-clock, receives the first money awarded by the Board of Longitude (23 years after the Act to create the Board). Harrison received 500 Pounds, 250 Pounds to be paid immediately, and another 250 Pounds after completing a second clock that passes testing at sea. *Derek Howse, Britain's Board of Longitude: The Finances 1714-1828
1742 Euler replied (see June 7 post) in a letter dated 30 June 1742, and reminded Goldbach of an earlier conversation they had ("...so Ew vormals mit mir communicirt haben.."), in which Goldbach remarked his original (and not marginal) conjecture followed from the following statement, “Every even integer greater than 2 can be written as the sum of two primes,” which is thus also a conjecture of Goldbach. In the letter dated 30 June 1742, Euler stated:“Dass ... ein jeder numerus par eine summa duorum primorum sey, halte ich für ein ganz gewisses theorema, ungeachtet ich dasselbe necht demonstriren kann.” ("every even integer is a sum of two primes. I regard this as a completely certain theorem, although I cannot prove it.")*Wik
As of this date, no one else has proved it either. It is one of the oldest open questions in mathematics.
1812 Congress authorized the President of the US to issue interest bearing Treasury Notes for the first time in history. The interest was fixed at "five and two-fifths per centum a year." *Kane, Famous First Facts (students might calculate the present value of a $100 investment on that date compounded to the present)
1808 Humphry Davy announced he had separated the element boron. However, working independently, French chemist, Joseph Louis Gay-Lussac had announced* the same accomplishment nine days ealier, on 21 Jun 1808. *TIS 1860 Oxford evolution debate took place at the Oxford University Museum on 30 June 1860, seven months after the publication of Charles Darwin's On the Origin of Species. Several prominent British scientists and philosophers participated, including Thomas Henry Huxley, Bishop Samuel Wilberforce, Benjamin Brodie, Joseph Dalton Hooker and Robert FitzRoy.
The debate is best remembered today for a heated exchange in which Wilberforce supposedly asked Huxley whether it was through his grandfather or his grandmother that he claimed his descent from a monkey. Huxley is said to have replied that he would not be ashamed to have a monkey for his ancestor, but he would be ashamed to be connected with a man who used his great gifts to obscure the truth *Wik
1894 Tower Bridge opens, In 1886, the foundation stone of the Tower Bridge in London, England was laid (over a time capsule) by the Prince of Wales. The need to cross the River Thames at this point had become increasingly urgent for many years, and finally the necessary Act was passed in 1885. The bridge, designed by Mr. Wolfe Barry, CB, was completed at a cost of about £1,000,000. To permit the passage of tall ships between the towers, two bascule spans, each of 100-ft length, are raised. The side spans to the towers are of the more familiar suspension type. Pedestrians can traverse a high-level footway nearly at the top of the towers, even when the bridge is raised. It was officially opened 30 Jun 1894, by the Prince of Wales, later Edward VII, on behalf of Queen *TIS
1908 A Comet(?) explodes above Tunguska, Siberia. *VFR In 1908, at around 7:15 am, northwest of Lake Baikal, Russia, a huge fireball nearly as bright as the Sun was seen crossing the sky. Minutes later, there was a huge flash and a shock wave felt up to 650 km (400 mi) away. Over Tunguska, a meteorite over 50-m diameter, travelling at over 25 km per second (60,000 mph) penetrated Earth's atmosphere, heated to about 10,000 ºC and detonated 6 to10 km above the ground. The blast released the energy of 10-50 Megatons of TNT, destroying 2,200 sq km of forest leaving no trace of life. The Tunguska rock came out of the Taurid Meteor storm that crosses Earth's orbit twice a year. The first scientific expedition for which records survive was made by Russian mineralogist Leonid Kulik in 1927. *TIS
1946 ENIAC formally accepted by the government. See 2 October 1955*VFR
In 1948, the transistor was demonstrated by its inventors, John Bardeen and Walter Brattain, scientists at the Bell Telephone Laboratory in Murray Hill, NJ.* It was a simple, tiny device utilizing the electronic semiconducting properties of a germanium wafer. The transistor represented a significant advance in technology. As it was developed over the next few years, it was incorporated into electronic equipment as a functional replacment for the vacuum tube. Such use of transistors provided great savings in space and electrical power consumption. This made possible the small portable, battery-powered transistor radios which were sold to the public by late 1954.*TIS
1954 Solar eclipse in Britain. The about 3 minutes totality was visible in the Faroes and the southern line was crossing the northernmost Shetland. Many people in England do remember this eclipse and is often mistaken as total for those who saw a large partial eclipse. The eclipse track traveled across Norway, Sweden, Lithuania, Byelorussia, and Russia. *NSEC
1955 Sperry Rand formed. In 1955 Sperry acquired Remington Rand and renamed itself Sperry Rand. Acquiring then Eckert-Mauchly Computer Corporation and Engineering Research Associates along with Remington Rand, the company developed the successful UNIVAC computer series and signed a valuable cross-licensing deal with IBM. *Wik
2011 Mr Ballew finally hung up his spurs and rode off into the sunset with his sweetheart, Jeannie.

BIRTHS

1748 Dominique Cassini (30 June 1748 – 18 October 1845) was a French mathematician and surveyor who worked on his father's map of France. He was the son of César-François Cassini de Thury and was born at the Paris Observatory. In 1784 he succeeded his father as director of the observatory; but his plans for its restoration and re-equipment were wrecked in 1793 by the animosity of the National Assembly. His position having become intolerable, he resigned on September 6, and was thrown into prison in 1794, but released after seven months. He then withdrew to Thury, where he died fifty-one years later.
He published in 1770 an account of a voyage to America in 1768, undertaken as the commissary of the French Academy of Sciences with a view to testing Pierre Le Roy’s watches at sea. A memoir in which he described the operations superintended by him in 1787 for connecting the observatories of Paris and Greenwich by longitude-determinations appeared in 1791. He visited England for the purposes of the work, and saw William Herschel at Slough. He completed his father’s map of France, which was published by the Academy of Sciences in 1793. It served as the basis for the Atlas National (1791), showing France in departments.
Cassini’s Mémoires pour servir à l’histoire de l’observatoire de Paris (1810) embodied portions of an extensive work, the prospectus of which he had submitted to the Academy of Sciences in 1774. The volume included his Eloges of several academicians, and the autobiography of his great-grandfather, Giovanni Cassini.*Wik 1791 Félix Savart (June 30, 1791, Charleville-Mézières, Ardennes – March 16, 1841, Paris) became a professor at Collège de France in 1836 and was the co-originator of the Biot-Savart Law, along with Jean-Baptiste Biot. Together, they worked on the theory of magnetism and electrical currents. Their law was developed about 1820. The Biot-Savart Law relates magnetic fields to the currents which are their sources. Félix Savart also studied acoustics. He developed the Savart wheel which produces sound at specific graduated frequencies using rotating disks.
Félix Savart is the namesake of the unit of measurement for musical intervals, the savart, though it was actually invented by Joseph Sauveur.*Wik1856 Cargill Knott (June 30, 1856 – October 26, 1922) born. He graduated from Edinburgh University and was then an assistant in the Physics department. With Barclay and Fraser he was one of the writers who originally proposed the founding of the EMS. He went to the Imperial University in Tokyo as Professor. He returned to a lectureship in Edinburgh and eventually became a Reader in Applied Mathematics. He became Secretary and Treasurer of the EMS in 1883 and President in 1893 and 1918.*SAU 1880 Birthdate of Rudolf Fueter (30 June 1880 in Basel; 9 August 1950 in Brunnen) who worked with functions with non-commutative variables and also in number theory. *SAU

DEATHS

1660 William Oughtred, (5 March 1575 – 30 June 1660) inventor of the slide rule (1621) and a staunch royalist, died in a transport of joy on hearing the news of the restoration of Charles II. Augustus De Morgan later remarked, “It should be added, by way of excuse, that he was eighty-six years old.” *VFR an Episcopal minister who invented the earliest form of the slide rule, two identical linear or circular logarithmic scales held together and adjusted by hand. Improvements involving the familiar inner rule with tongue-in-groove linear construction came later. He introduced the familiar multiplication sign x in a 1631 textbook, along with the first use of the abbreviations sin, cos and tan.*TIS 1919 John William Strutt 3rd Baron of Rayleigh (of Terling Place)(12 November 1842 – 30 June 1919) was an English physical scientist who made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He received the Nobel Prize for Physics in 1904 for his investigations into the densities of the most important gases and his successful isolation of argon, an inert atmospheric gas.*TIS

Friday, 29 June 2012

The 181st day of the year; 181 is the 9th palindromic prime number.The next prime number is 191, and also a palindrome. *Prime Curios (Is there another pair of consecutive primes which are both palindromes?)

EVENTS

In 3123 BC, a Sumerian astronomer saw a devastating asteroid, perhaps a half-mile wide, according to an interpretation of a clay tablet, made by researchers from Bristol University, reported in The Times on 31 Mar 2008. The ancient date was indicated by a computer recreation of the night sky using symbols on the tablet recording the positions of constellations The Planiform tablet found by Henry Layard at Nineveh, likely a 700 BC copy of the astronomer's notes, described in cuneiform a "white stone bowl approaching" that "vigorously swept along." The asteroid probably crashed into the Austrian Alps, leaving a swath of cataclysmic damage such as, for example, the Genesis destruction of Sodom and Gomorrah.*TIS 1803 An open letter to the public, and the Congress of the United States on the topic "Of The Construction of Iron Bridges" is posted by Thomas Paine. Paine had discussed this work with President Jefferson in a letter while he was in England. *The National Intelligencer and Washington Advertiser, (Washington, DC) Wednesday, June 29, 1803; Issue CCCCXIX; col B
Of the Construction of Iron Bridges
1927 Gellivara 1073: Minor planet discovered September 14, 1923 by Johann Palisa at Vienna. Named for the small town Gällivare in Swedish Lapland where in the year 1927 astronomers from several countries observed the Total Solar Eclipse of 1927 Named by the astronomer J. Rheden and endorsed by Anna Palisa.*NSEC1877 After proving that the points in a square can be put in one-to-one correspondence with the points on a line segment Cantor wrote his friend Dedekind “Je le vois, mais je ne le crois pas.” (I see it, but I don’t believe it.) [Dauben, Georg Cantor, p. 55]*VFR

In 1954, the Atomic Energy Commission, by a vote of 4 to1 decided against reinstating Dr. J. Robert Oppenheimer's access to classified information. The Atomic Energy Act of 1946 required consideration of "the character, associations, and loyalty" of the individuals engaged in the work of the Commission. Substantial defects of character and imprudent and dangerous associations, particularly with known subversives who place the interests of foreign powers above those of the United States, were considered reasons for disqualification. The Commission regarded his associations with persons known to him to be Communists exceeded tolerable limits of prudence and self-restraint, and lasted too long to be justified as merely the intermittent and accidental revival of earlier friendships.*TIS

1956 The interstate highway system was signed into law by President Eisenhower. Even (odd) num­bered roads run East–West (North–South) with the numbers increasing from South to North (West to East). Roads with three digit numbers are loops around cities (when the ﬁrst digit is even) or spurs (ﬁrst digit odd); In either case the last two digits are the main road number. *VFR

In 1956, the Act that made possible the modern interstate highway system in the U.S. was signed by President Dwight D. Eisenhower. Eisenhower had seen the speed and efficiency in moving troops and equipment on the four-lane autobahns in Germany during WW II. The idea of federal support of interstate limited-access routes in the U.S. had begun with a study under the Federal-Aid Highway Act of 1938. Little progress was made on building these roads while federal funding was low. When the Federal-Aid Highway Act of 1956 committed federal funds to the States for 90% of the cost, construction began in earnest for the System of Interstate and Defense Highways having at least four lanes with no at-grade railroad crossings. *TIS

2012 - My Jeannie is celebrating her birthday today, and I'm celebrating having her in my life... all the good I ever do is a reflection of a single sun.

BIRTHS

1818 Pietro Angelo Secchi (29 June 1818 – 26 February 1878) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall. *TIS 1868 George Ellery Hale (June 29, 1868 – February 21, 1938) born. American astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200" reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him - the Hale telescope.*TIS 1893 Eduard Cech, (June 29, 1893 – March 15, 1960) Czech topologist. Czech mathematician born in Stračov, Bohemia (then Austria-Hungary, now Czech Republic). His research interests included projective differential geometry and topology. In 1921–1922 he collaborated with Guido Fubini in Turin. He died in Prague. *Wik

1904 Topologist Witold Hurewicz (June 29, 1904 - September 6, 1956)born. Hurewicz is best remembered for two remarkable contributions to mathematics, his discovery of the higher homotopy groups in 1935-36, and his discovery of exact sequences in 1941. His work led to homological algebra. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from groups, which were obviously commutative...". *Wik He died in 1956 when he fell off a pyramid while attending a conference in Mexico.

1942 K. Jon Barwise (June 29, 1942 – March 5, 2000) an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.*Wik

DEATHS

1895 T(homas) H(enry) Huxley (4 May 1825 – 29 June 1895) was an English biologist , known as "Darwin's Bulldog" for his promotion of Darwinism which led him to an advocacy of agnosticism (a word he coined). At the age of 12 he was reading advanced works on geology, and by early adolescence he recorded the results of simple self-conducted experiments. As a ship's assistant surgeon on HMS Rattlesnake he studied marine specimens by microscope. During the 1850's he published papers on animal individuality, the cephalous mollusks (ex. squids), the methods of paleontology, and the methods and principles of science and science education. *TIS 1924 Robert Simpson Woodward(July 21, 1849–June 29, 1924) was an American physicist and mathematician, born at Rochester, Michigan. He graduated C.E. at the University of Michigan in 1872 and was appointed assistant engineer on the United States Lake Survey. In 1882 he became assistant astronomer for the United States Transit of Venus Commission. In 1884 he became astronomer to the United States Geological Survey, serving until 1890, when he became assistant in the United States Coast and Geodetic Survey. In 1893 he was called to Columbia as professor of mechanics and subsequently became professor of mathematical physics as well. He was dean of the faculty of pure science at Columbia from 1895 to 1905, when he became president of the Carnegie Institution of Washington, whose reputation and usefulness as a means of furthering scientific research was widely extended under his direction. He was elected to the National Academy of Sciences in 1896. In 1898-1900 he was president of the American Mathematical Society, and in 1900 president of the American Association for the Advancement of Science. In 1915 he was appointed to the Naval Consulting Board. He died in 1924 in Washington, D.C.*Wik

Thursday, 28 June 2012

The following includes most of a note in the Analyst regarding Hamilton's meaning for the name Quaternions. It includes a poem it appears he wrote, which I had never seen.
Hope it is enjoyable to others.

ORIGIN OF THE NAME "QUATERNIONS".

BY PROF. W. W. JOHNSON, ANNAPOLIS, MD.

clipped from article:

It appears from the Preface to the "Lectures" (see page 47), that the four units are the heterogeneous quantities 1, i, j and k, of which the first is the real or scalar unit, and the others correspond to three
mutually rectangular directions in space. Hamilton had in fact found that expressing directed lines in the triplex form ix +jy + kz, x, y and z being real coefficients, he was able to interpret their product as of the form w+ix+jy+kz, a quadruplex quantity, viz.?the sum of a number and line, the latter being perpendicular to the plane of the factor lines.
It seems to have been a favorite conception of Hamilton's to refer the real quantities of simple Algebra to the uni-dimensional quantity time, as in his Essay on Algebra as the Science of Pure Time; thus in the combination of line and number to which his investigations led him, he saw united the one of time and the three of space, as expressed in the sonnet below, which was published after his death in an Article upon the life and genius of Hamilton, in the North British Review.

Sonnet by the Inventor of Quaternions.

(Supposed to have been addressed to Sir John Herschel.)

The Tetractys,
Or high Matheis, with her charm severe
Of line and number, was our theme; and we
Sought to behold her unborn progeny,
And thrones reserved in Truth's celestial sphere:
While views, before attained, became more clear;
And how the One of Time, of Space the Three,
Might, in the chain of Symbol, girdled be:
And when my eager and reverted ear
Caught some faint echoes of an ancient strain,
Some shadowy outlines of old thoughts sublime,
Gently he smiled to see, revived again,
In later age, and occidental clime,
A dimly traced Pythagorean lore,
A westward floating, mystic dream of four.

From "The Analyst Vol. 7, No. 2, Mar., 1880

Thony Christie sent the following comment shortly after I posted this :William Wordsworth who was a good friend of Hamilton's when asked for his opinion on H's poetry told him he should stick to mathematics.

In my opinion, a mathematician, in so far as he is a mathematician, need not preoccupy himself with philosophy -- an opinion, moreover, which has been expressed by many philosophers.

Henri Lebesgue

The 180th day of the year; 180 can be formed with the only the first two primes... 180 = 22 x 32 x (2+3) *Prime Curios

EVENTS

1451 Sort of the American version of the Medes and Lydians. The Seneca and Mohawk tribes were preparing for war when a total solar eclipse swept over both their camps late in the afternoon of this early summer day. Both immediately sued for peace. (ref. DB 6/97: "A star Called the Sun" by George Gamow). *NSEC 1489 Last total solar eclipse on Easter Island. The next one will occur on 11 July 2012 and thereafter on 25 February 2324. Ref. More Mathematical Astronomical Morsels by Jean Meeus; Willmann-Bell, 2002. *NSEC 1751 The ﬁrst volume of Diderot’s and d’Alembert’s Encyclopedie appeared. See Hawkins, Jean d’Alembert p. 69.*VFR 1832, the first American case of a cholera epidemic was reported in New York City. Previously, Europe and the Americas were unaffected by the First Cholera pandemic of 1817 when cholera, long endemic to the Indian subcontinent, spread to Arabia, Syria, and southern Russia. This abated in the early 1820's, but a new cholera cycle began in 1826. It invaded the British Isles in Oct 1831. Canada was struck shortly before cholera reached New York. Cholera was a horrible disease, spread through fouled water. Its victims died after hours of cramps, diarrhea, and vomiting. Crowded into unsanitary slums, the poor suffered most. Many of the city's elite fled to the countryside. In America, the disease's hold broke by Dec 1832.*TIS1884 Sonya Kovalevskaya officially appointed extraordinary professor at Stockholm University. [The Mathematical Intelligencer, vol. 6, no. 1, p. 29; *VFR ]In 1958, the Mackinac Bridge, the world longest suspension bridge, was dedicated. Ceremonies began on 24 Jun with the first "Governor's Walk" across the bridge. (It had opened to traffic on 1 Nov 1957.) This bridge joins the upper and lower peninsulas of the state of Michigan, reducing the crossing time, from a couple of hours, to just 10 minutes. Ceremonial groundbreaking took place at the St. Ignace end of the bridge on 7 May 1954, and on the opposite shore at Mackinaw City the next day. Meanwhile caissons and superstructures were assembled as far away as Indiana, Pennsylvania and Ohio. Including approaches, the total length is 26,444-ft, needing 34 bridge support foundations. The main span is 3,800-ft long. *TIS 2009 Stephen Hawking gave a party for time travelers at 12:00 UT on this day. He did not announce the event until after it was over, and it appears that no one else cared to attend. Below is the invitation, so if you missed it up until now, it's not to late to choose not to attend. (So much for free will)

*daily Mail online 2011 "6.28" has become popular as Tau day with many people who think 2 pi (or 6.28...) is more appropriate, or just a nice addition to Pi-day, on March 14 (or 3.14... )

Births

1768 George Hadley (12 Feb 1685; 28 Jun 1768 at age 83) English physicist and meteorologist who first formulated an accurate theory describing the trade winds and the associated meridional circulation pattern now known as the Hadley cell.*TIS Hadley died at Flitton and was buried in the chancel of Flitton church. 1875 Henri Lebesgue (June 28, 1875 – July 26, 1941) He introduced the concept of Lebesgue Measure, a device for measuring the ‘length’ of complicated sets of points on the line, and so is known as the father of modern integration theory. *VFR French mathematician whose generalization of the Riemann integral revolutionized the field of integration. He was maître de conférences (lecture master) at the University of Rennes until 1906, when he went to Poitiers, first as chargé de cours (assistant lecturer) of the faculty of sciences and later as...*TIS1894 Einar Hille (28 June 1894 – 12 February 1980) born. In the preface of his Analytic Function Theory (1959) he wrote “It is my hope that students of this book may come to respect the historical continuity of the subject.” More authors should include historical footnotes as good as those in this book.*VFR Hille's main work was on integral equations, differential equations, special functions, Dirichlet series and Fourier series. Later in his career his interests turned more towards functional analysis. His name persists among others in the Hille–Yosida theorem. *Wik1920 Nicolaas Hendrik "Nico" Kuiper (28 June 1920, Rotterdam - 12 December 1994, Utrecht) was a Dutch mathematician, known for Kuiper's test and proving Kuiper's theorem. He also contributed to the Nash embedding theorem.
Kuiper completed his Ph.D. in differential geometry from the University of Leiden in 1946 under the supervision of Willem van der Woude.
He served as director of the Institut des Hautes Études Scientifiques from 1971 to 1985.*Wik1972 Ngô Bảo Châu (June 28, 1972 - ) is a Vietnamese and French mathematician at the University of Chicago, best known for proving the fundamental lemma for automorphic forms proposed by Robert Langlands and Diana Shelstad. In 2004, Chau and Laumon were awarded the Clay Research Award for their achievement in solving the fundamental lemma proposed by Robert Langlands for the case of unitary groups. Chau also became the youngest professor in Vietnam in 2005. His proof of the general case was selected by Time as one of the Top Ten Scientific Discoveries of 2009. In 2010, he received the Fields Medal and in 2012, the Legion of Honour He is the first Vietnamese to receive the Fields Medal *Wik

DEATHS

1889 Maria Mitchell (August 1, 1818 – June 28, 1889) First American professional woman astronomer, born Nantucket, Mass. While pursuing an amateur interest, on 1 Oct 1847, she gained fame from the observation of a comet which she was first to report. She was also the first female member of the American Association of Arts and Sciences. She died at age 70 in Lynn, Mass.

1930 William J Greenstreet graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette.

One of the most significant personalities among Hungarian mathematicians.

At the beginning he studied engineering at the Technical University of Zurich, but he soon realised that he was much more interested in mathematics than in technical subjects. So he continued to study at the Royal Hungarian University of Sciences in Budapest. For him the lectures of Gyula Kőnig and József Kürschák meant the most. Then he learnt for a year in Göttingen and attended the lectures of David Hilbert and Hermann Minkowski. He obtained his PhD degree and diploma of secondary school teacher of mathematics and physics in Budapest.

1952 William Watson graduated in Mathematics and Physics from Edinburgh University. He became head of the Physics department at Heriot Watt College in Edinburgh.*SAU

1984 Claude Chevalley (11 February 1909, Johannesburg – 28 June 1984, Paris) had a major influence on the development of several areas of mathematics including Ring Theory and Group Theory *SAU

1974 Vannever Bush ( March 11, 1890 – June 28, 1974) American electrical engineer and administrator who and oversaw government mobilization of scientific research during World War II. At the age of 35, in 1925, he developed the differential analyzer, the world's first analog computer. It was capable of solving differential equations. He put into concrete form that which began 50 years earlier with the incomplete efforts of Babbage, and the theoretical details developed by Kelvin. This machine filled a 20 x 30 foot room. He innovated one of the largest growing media in our time, namely hypermedia as fulfilled in the Internet with hypertext links *TIS

Wednesday, 27 June 2012

Recently, with thanks to the folks at JSTOR who have made many of the older issues of The American Mathematical Monthly available without subscription, I have been reading through some of the early issues.
This morning I came across two interesting circle problems that looked both interesting, and challenging to the typical High School student, so here they are. I will wait a couple of days and post the answers.

Enjoy,

18. Proposed by L. B. HAYWARD Superintendent of schools Bingham, Ohio:
In a circle whose radius is 6, find the area of the part between parallel chords
whose lengths are 8 and 10, both being on the same side of the center.

17. Proposed by H. W. HOLYCROSS, Superintendent of Schools, Pottersburg Union County, Ohio:
A gentleman owns a circular farm, and if three circles of equal area and as
large as possible be drawn within it, the circular area in the center of the farm will
contain one acre; what is the area of the circular farm ?

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I'm a retired math teacher, calc-stats-the regular stuff... Interested in Math, math history, and assorted other curiosities.Married and in love with a gorgeous woman. I have a math page on the etymology of math terms, and another, On This Day in Math, which covers historical events related to the current date.